The performance of many mechanical-structural systems, such as aircraft wings and antenna reflectors, is directly related to the geometric shapes of their components. Such systems would ideally prefer to adopt different shapes for different operating conditions, but they are generally designed to have one fixed shape that constitutes a compromise with respect to all the operating conditions. Research in reconfigurable surfaces aims to address this problem by providing ways to dynamically reconfigure the shape of the material surface in order to respond to varying operating conditions and external disturbances. This capability will enable systems such as aircrafts to maintain optimal performance and enhance versatility.
The most common approach to morph structures is based on compliant mechanisms. A compliant mechanism is a single piece of flexible structure that delivers the desired motion by undergoing elastic deformation as opposed to the rigid body motions in a conventional mechanism. These mechanisms are flexible enough to transmit motions, yet stiff enough to withstand external loads. The hinge-less nature of compliant mechanisms eliminates the backlash error and effectively reduces the production and maintenance costs associated with systems. Moreover, the distributed compliance throughout the compliant mechanism provides a smooth deformation field, which reduces the stress concentration.
Previous research on compliant mechanism synthesis has typically employed a two-step synthesis approach. The two-step approach decomposes the interrelated topology and dimensional syntheses into two separate stages: first, topology synthesis ensures the motion in the desired output direction and, second, the size and geometry optimization refines the mechanism dimensions to achieve a desired objective such as maximizing displacement. There are successful demonstrations of morphing structures based on the idea of compliant mechanisms.
One promising approach for creating large deformation morphing structures is based on using variable-stiffness components to provide large deformation without large energy input to the system. A variable-stiffness structure consists of constant stiffness material layers and variable modulus material layers arranged in alternating layers. The variable modulus material layers have a material with an elastic modulus that changes in response to an applied energy field. This allows reversible coupling and decoupling of stress transfer between successive layers of the constant stiffness material layers, providing a change in a bending stiffness of the variable-stiffness structure.
Variable-stiffness components create an ill-posed design problem and generally have multiple solutions for any given morphing task. Previous approaches to the solution of this complex problem related to the design of compliant mechanisms for morphing structural shapes. These approaches are inferior for the following two reasons.
First, the previous approaches are not well-suited for large deformation morphing tasks. This is because the amount of elastic energy consumed in morphing with large deformation using these compliant mechanisms is prohibitively large and makes it impractical to implement on real systems. In addition, these mechanisms cannot accomplish significant “Gaussian Curvature” or simultaneous curvature about two orthogonal axes because this requires a change in area in the plane of the deformation.
Second, the assumptions made in the previous methods are oversimplified. Some of these assumptions include the requirement that the shape-changing object will change from its initial profile to only one target profile and that the compliant mechanism has only a single external input actuator at a specified location. These assumptions are far too restrictive for any general-purpose morphing task.
Thus, a continuing need exists for a method that formulates the morphing problem as an optimization search, efficiently searches the design space and rapidly arrives at a family of plausible solutions. Such a method should be capable of operating on variable-stiffness components and thus offer solutions for more complex shapes, non-limiting examples of which include those shapes that can have large deformations, such as complete foldings. Such a method should also be completely unrestrictive with regard to any design constraints and thus offer a more powerful solution for design of morphing strategies that can realize complex target shapes using reconfigurable surfaces.